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Quantum Physics

Title:
Quantum circuits of T-depth one

Abstract: We give a Clifford+T representation of the Toffoli gate of T-depth 1, using
four ancillas. More generally, we describe a class of circuits whose T-depth
can be reduced to 1 by using sufficiently many ancillas. We show that the cost
of adding an additional control to any controlled gate is at most 8 additional
T-gates, and T-depth 2. We also show that the circuit THT does not possess a
T-depth 1 representation with an arbitrary number of ancillas initialized to 0.